Determination of the load-bearing capacity of natural-stone masonry arches is an important aspect in the field of conservation of architectural heritage. Structural verification of bridges of this type requires thorough methods in order to make efficient use of the considerable reserve commonly found in their structural capacity. The failure of these structural elements often involves successive formation of hinges until failure. The present study aims to establish a novel analytical model to evaluate the load-bearing capacity of stone masonry arch bridges. The model takes into account both the non-linear behaviour of masonry and the high ductility of such arches. Furthermore, the analysis considers the effect of typical deficiencies of masonry arches on their load-bearing capacity. The application of the developed model is illustrated in a case study.